Non-markov General Model of the Functioning of the Robot Control System in Changing Environmental Conditions

Gusenitsa, Ya.N.; Shiryamov, Oleg; Rzhavitin, Vyacheslav; Buryj, Dmitriy; Ljvov, Dmitriy

doi:10.1007/978-3-031-20631-3_5

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Cited by 2 publications

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“…These include polymers with extended volume [5], first-passage problems in three dimensions [10], the Kramers problem in diffusion [12,17], and population genetics models [9]. Non-Markovian processes have manifold applications in many fields, including robotics [11], thermodynamics [22], and atomic physics [15].…”

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confidence: 99%

On options pricing under a quadratic stochastic process modulated GBM model

2023

Advances in the Theory of Nonlinear Analysis and Its Application

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This paper deals with the European option-valuation problem under a prediction model for the underlying asset prices with an external impact. We suggest an alternative model for risky asset prices in which the parameters are dependent on a non-Markovian process. This generalizes the regime-switching models with continuous-time Markov-chain processes. A notable problem of this model is that the process embedded in the parameter of the stock price is non-Markovian; in addition, the market is incomplete. The change from the historical probability to a risk-neutral one is investigated, and the set of equivalent martingale measures is determined. In addition, an infinitesimal generator is obtained, which allows numerical simulations of the non-Markovian and the stock-price processes to be conducted. Several illustrations are provided.

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